The most famous mathematicians are generally the most famous mechanics.

the two disciplines of mathematics and mechanics are a bit like a pro-sister. They grow together in a companion. In the long river of historical development, the development of mainstream mathematics and mechanics is always synchronous. On the one hand, the breakthrough means that on the other hand there is a leap.

before the 16th century, the mainstream of mechanics was statics, and the corresponding mathematics were Euclidean geometry and simple algebraic operations. By 16th century, the dynamics of the study, the corresponding mathematical development of mathematical variables, namely, calculus, geometric development is analytic geometry, especially the corresponding to the planetary orbit of understanding, about two times the geometry of the curve has been fully developed. In the 17th century and 18th century, with the development of analytical mechanics, the variational method developed, with the formation of the concept of multiple degrees of freedom in the mechanical system, the geometry has the development of manifold and Riemannian geometry. By the 19th century, due to the development of continuum mechanics, i.e., elasticity and fluid mechanics, and heat transfer, partial differential equations have also developed rapidly.

The characteristics of the two disciplines in the development of mathematics and mechanics can not be reflected in the characteristics of the representative figures of the two disciplines. We can see that the most famous mathematicians in history are also the most famous mechanics at the same time.

1. The most eminent six-bit mathematical mechanics

If you were to choose six of the most famous mathematicians around the world by 19th century. Who would you choose. I think most people would choose this six: Archimedes, Newton, Leibniz, Euler, Lagrange, Cauchy.

but you thought, these six are also the top mechanics. For their life, because of their great fame, everyone has a special biography, we do not want to repeat their contribution. They are a master of both mathematics and mechanics.

Archimedes (Archimedes, 287 BC---212BC), the earliest master of mechanics, is known as "the father of the discipline of mechanics". The most notable contributions in mechanics are: the buoyancy principle of the liquid, the calculation method of the center of gravity of a series of graphs, the lever principle based on rigorous argumentation, the equilibrium stability condition of the parabolic rotating body on the liquid surface.

in mathematics, he gives the calculation method of the volume and center of gravity of the curve around a simple figure, thus introducing a simple limit concept.

Newton (ISAAC newton,1642,12,25-1727,3,20). In mechanics, he is the founder of the law of free particle movement and the founder of celestial mechanics. He was later called the founder of classical mechanics. In a rigorous manner, he argues that, under the effect of gravitation, which is inversely proportional to the square of distance, the trajectory of the planet is elliptical and theoretically derives the Kepler law based on the observed planetary motion. Wrote a masterpiece called "The Mathematical Principles of natural Philosophy" in the annals of history.

He is one of the founders of calculus in mathematics.

These two achievements, in fact, are the cornerstone of modern science that has developed rapidly since the 16th century.

Leibniz (Gottfried Wilhelm leibniz,1646-1716) is a man of the same age as Newton. His well-known contribution to mathematics is the invention of calculus at the same time as Newton. His contribution to mechanics, however, is not very much noticed. In fact, his contribution to mechanics is the great influence of the conservation law of the kinetic energy of the proposed. Before Leibniz, people gave full attention to the expression of velocity, acceleration and momentum of particle motion, while Leibniz first noticed the kinetic energy of the motion of particles. As long as attention to the subsequent John Bernoulli (Johaun bernoulli,1667-1748) proposed and by the Coriolis precision of the principle of virtual work, the later analysis of the development of mechanics and the introduction of a series of effects in mechanics, can understand the implications of this concept far-reaching.

Leibniz, in addition to his special genius in mathematics and mechanics, has demonstrated excellence in many fields: law, religion, politics, history, literature, logic, and philosophy. However, he is not what people call "Master of Everything, everything is sloppy". And when people read the history of each of these aspects, they will encounter his name. So people say that Leibniz is the last all-rounder in human history.

Euler (Leonhard euler,1707-1783), in 1697, John Bernoulli his proposed maximum speed of the problem of extension, referred to the problem of short-range line. As a student under the guidance of John Bernoulli, Euler solved the problem at the age of 21 and, together with Lagrange, invented the mathematical tool of the variational method. Euler in mathematics, is a versatile, he in the three main branches of mathematics: analysis, Geometry and algebra have a groundbreaking contribution, he is also a versatile in mechanics, he in the mechanics of the three main branches: fluid mechanics, solid mechanics and general mechanics, have a groundbreaking contribution. In fluid mechanics, he gives the equation of motion for the ideal fluid. In general mechanics, he gives the Euler equation of rigid body motion. In the field of solid mechanics he gives the first solution to the nonlinear problem of elastic rods.

Lagrange (Joseph Louis Lagrange, 1736,1,25-1813,4,11) is the founder of analytical Mechanics and variational methods. The "Analytical mechanics", which he wrote over more than 20 years in 1788, is an epoch-making document in the history of mechanics. This book opens up the history of the binding science system. The Lagrange's coordinates and Lagrange's equations are the main results of this book. In addition, he also has important contributions in the fields of elasticity, fluid mechanics, celestial mechanics and so on.

we can clearly see the contribution of Lagrange in mathematics, such as variational method, partial differential equation, some basic theorems in mathematical analysis, etc., mainly revolves around him to completely solve his pursuit of analytical mechanics. However, he still has a lot of important work in the approximate solution of algebraic equations and the interpolation of functions.

Cauchy (cauchy,augustin-louis,1789,821-1857,523), in mechanics, he is the founder of elasticity. In mathematics, he is also the founder of the rigorous modern mathematical analysis.

The concept of strain and stress, the concept of equilibrium equation, and the concept of the generalized Hooke's law, which we introduced today in elastic mechanics, were introduced by Cauchy in the 20-30 's in 19th century. Cauchy in mathematics, the theory of partial differential equations and the theory of complex functions of the establishment of a groundbreaking work, so far people say that Cauchy initial value problem, Cauchy-Riemannian conditions, are the basic results in this respect.

from the six scholars mentioned above, it is true that their contribution is mainly based on mathematics or mechanics. We can only say that they are all mathematical mechanics, not simply to call them mathematicians or mechanics.

From here we can at least realize that, before 19th century, mechanics and mathematics were not separated. However, this cannot be said absolutely, this to the above-mentioned scholars of course is right, but for their scholars outside, can not generalize. For example, Galileo and Huygens, the main emphasis on mechanics, to the Lang Bell, Laplace, Hamilton, Gauss is mathematics and mechanics and long scholars, and such as Riemann, Weierstrass, Gamma MabThera and other mathematicians, the main results of emphasis on pure mathematics. In general, most of the famous mathematicians are mechanics, at least they are very familiar with mechanics.

2. The famous mathematician and mechanics of the 20th century

entering the 20th century, the knowledge of human beings is getting thinner and smaller, not only is the knowledge of the Leibniz as good as the common people seldom seen, even in the field of mathematics and mechanics like Euler across all major branches of mathematics and mechanics have made important contributions to the scholars are rare. Norbert wiener,1894-1964, an American scholar, in his 1948 book on Cybernetics, said: "No one seems to be able to fully grasp the full range of contemporary intellectual activity since Leibniz." Since then, science has increasingly become a specialists in the increasingly narrow field of business. In the last First century, there may be no such person as Leibniz, but there is a Gauss, a Faraday, a Darwin. Today there are few academics who call themselves mathematicians, or physicists, or biologists without any restrictions. A person can be a topology, an acoustic home, or a beetle-biologist. His mouth is the jargon of his field, he knows all the literature in that field, all the branches of that field, but he often sees the scientific problems of the neighborhood as irrelevant, and thinks that if he has any interest in the problem, it is not allowed to infringe on the behavior of the people's territory. "[1]

since the 20th century, a mathematician, even the main branch of mathematics is difficult to cross, whether in 20th century, the outstanding mathematicians and mechanics of the discipline of this insulation. I am afraid not to say so, due to the close kinship of mathematics and mechanics, from disciplines. The most famous mathematicians have made outstanding contributions to mechanics. We only cite the most famous three top mathematicians of the 20th century: Poincaré, Hilbert, and Kolmogorov as examples to illustrate this close relationship.

French mathematician Poincaré (Jules Henri poincaré,1854-1912), in the history of mathematics, he was the last person to dabble in various branches of mathematics, including pure mathematics and applied mathematics, so he was hailed as the last generalist in mathematics.

Poincaré used more energy in his life to study celestial mechanics, and he studied the motion problem that was abstracted as n particles interacting with gravitation, which is generally called N-body problem. When n=2 is resolved by Newton, the problem becomes extremely difficult when n equals greater than 3 o'clock. Poincaré 's three-volume masterpiece, "New Methods of Astrophysics" (1892, 1893, 1899) concentrates on his research on this issue. To solve this problem, the book contains a series of his new mathematical achievements, such as the limit cycle theory, the qualitative theory of differential equations, the resulting research and results of topology, dynamic system change of the number of equations and so on. His achievements mark the new historical period of the dynamical system from quantitative research to qualitative research. It can be said that these achievements, both belong to the results of mathematics and also belong to the results of mechanics.

The German mathematician Hilbert (divID Hilbert, 1862-1943), who has been extensively involved in mathematics, has worked on the fields of algebraic invariants, algebraic number theory, geometric foundations, and mathematical proofs. His report on the 23 questions of mathematics at the 1900 Paris World mathematicians conference almost influenced the entire 20th century mathematical study. However, Hilbert, although the main interest is mostly concentrated in the field of pure mathematics. However, his interest in mechanical and physical problems remains strong. What is particularly worth proposing is that his study of variational problems and integral equations leads to the establishment of the spectral theory of mathematical problems, the result of which is the later so-called Hilbert space theory. The importance of Hilbert space theory is to extend the principle of Euclidean geometry to function space, which lays a theoretical foundation for the solution and qualitative discussion of continuous medium mechanics problem. Another important aspect of Hilbert's physics is the axiomatic approach to physical problems, which is the sixth issue in his 23 questions, and after nearly a century of effort, the axiomatic approach has been very successful in quantum mechanics, thermodynamics and other fields. And he has done very important work on the axiomatic of general relativity.

Russian mathematician Kolmogorov (а.н.колмогоров,1903-1987), he has a strong interest in mathematics and practical problems as well as mathematics education. He has important achievements in trigonometric series, genetics, probability theory, stochastic process, turbulence, dynamical system, information theory, mathematical logic, computational complexity, functional analysis, metal science and so on. In the the 1930s, he was the founder of the axiomatic system of probability theory, and then made a groundbreaking achievement in theory and application of probability theory and stochastic process.

in the study of mechanics, the most important result is that in 1941, the law of the attenuation of energy in turbulence and the compliance relation of pulsating frequency were obtained, which is called Kolmogorov law.

in the the mid 1950s, he concentrated on the question of whether the solar system could develop forever without causing catastrophe in classical mechanics. Does a simple galaxy have only three-body systems to move stably? This problem is attributed to the study of the motion system of an approximate integrable system. Poincaré called it the development of the Hamiltonian system under perturbation. It is the fundamental problem of dynamics, which can be traced to Newton's and Laplace's research. In the 50 's, Kolmogorov solved the problem with a large number of initial conditions, and pioneered the perturbation theory of Hamiltonian system. From his theorem, it is possible to launch a satellite orbiting Jupiter in orbit that does not affect Jupiter's elliptical orbit under the interference of Jupiter's motion along an elliptical orbit. His theory can also be used in a large number of mechanical and physical problems, which solves the problem of the stability of high-speed rotation of asymmetric rigid body around fixed point and the stability of magnetic surface in tokamak (токамак) type System. His thoughts were later a. И Arnold and J. Moser developed into a Kam theory named after the three of them. In addition, he also applies information theory to the Ergodic property of dynamical system, and obtains some important results.

from the experience of the three mathematicians we have briefly introduced, we can see that even in the 20th century, the research achievements of the first-rank mathematicians were closely related to mechanics, or a subject with strong mechanical background.

3. Fundamentals of the Mechanics discipline

In another article, "Contributions to the mechanics of several great physicists," we introduced the mechanical contributions of seven of the first-rank modern physicists, stating that tradition is essential for real scientific progress. The revolutionary change of modern physics and science is not produced in a vacuum, it is developed on the basis of inheriting traditional classical mechanics. They are therefore able to have a deep mechanical foundation and excellent performance. And their understanding of the importance of the discipline of mechanics. It also shows that these physicists understand the role of mechanics from the height of methodology. It is based on a deep understanding of the importance of mechanics that drives them to play a strong foundation in action and to make outstanding contributions.

in this paper, we also introduce the work of the famous mathematician and the close connection of mechanics. As for the mechanics and the close relationship between the engineering technology, it is self-evident.

Ultimately, mechanics is inseparable from physics and mathematics. It can also be said that mechanics is a more basic discipline in all basic disciplines. It is impossible for a nation and a nation to reach a considerable height in modern science and technology, without a solid mechanics education and without a certain high level of mechanical research.

The most famous mathematicians are generally the most famous mechanics.